Q. 94.2( 44 Votes )
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term.
Answer :
Now, By using nth term of an A.P. formula
tn = a + (n – 1)d
where n = no. of terms
a = first term
d = common difference
tn = nth terms
Given: t9 = 0
⇒ t9 = a + (9 – 1)d
⇒ 0 = a + 8d
⇒ a = – 8d
To Show: t29 = 2× t19
Now,
⇒ t29 = a + (29 – 1)d
⇒ t29 = a + 28d
⇒ t29 = – 8d + 28d = 20 d (since, a = – 8d )
⇒ t29 = 20 d
⇒ t29 = 2 × 10 d ….(1)
Also,
⇒ t19 = a + (19 – 1)d
⇒ t19 = a + 18d
⇒ t19 = – 8d + 18d = 10 d (since, a = – 8d )
⇒ t19 = 10 d …..(2)
From eq. (1) and eq. (2) we get,
t29 = 2× t19
Rate this question :
Champ Quiz | Arithmetic Progression30 mins
Champ Quiz | Arithmetic Progression34 mins
Quiz | Arithmetic Progression44 mins
Smart Revision | Arithmetic Progression47 mins
Smart Revision | General Term of an A.P44 mins
Master Arithmetic Progression36 mins
Lets Check Your Knowledge in A.P.49 mins
Quiz on Arithmetic Progression Quiz32 mins
Get to Know About Geometric Progression41 mins
NCERT | Solving Questions on Introduction of A.P42 mins
Attempt any two subquestions form the following:
If the second term and the fourth terms of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:
Maharashtra Board - Algebra PapersAttempt any five of the following sub questions:
Find a sequence if 
then find the value of S10.
Attempt any two of the following subquestions:
If the sum of first p terms of an A.P. is equal to the sum of first q terms, then show that the sum of its first (p + q) terms is zero where p#q.
Maharashtra Board - Algebra PapersAttempt any two subquestions from the following:
Find the sum of all numbers from 50 to 350 which are divisible by 4. Also find 15th term.
Maharashtra Board - Algebra PapersAttempt any four of the following subquestions:
Find the first two terms of the sequence for which Sn is given below: Sn = n2 (n + 1).
Maharashtra Board - Algebra PapersIf first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is 
If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)
MHB - Mathematics Part-1Find the sum of all even numbers from 1 to 350.
MHB - Mathematics Part-1